standards for mathematical practice - digital chalkboard · “mathematics: kindergarten through...

California Department of Education 1

Talking Points:

• Welcome to the “Mathematics: Kindergarten through Grade Twelve Standards for Mathematical Practice”

module, a part of the Common Core State Standards (CCSS) for California Educators Professional

Learning Module Series.

• There are two math modules: This module, which covers mathematical practices, and another titled,

“Mathematics: Kindergarten through Grade Eight Learning Progressions” which covers the kindergarten

through grade eight content standards for mathematics.

• This module explores the teaching and learning of mathematics through the lens of the Standards for

Mathematical Practice for students in kindergarten through grade twelve. It will deepen educators’

understanding of what the mathematical practices are, and why they are important to bring to their

students as they transition to the CCSS.

California Department of Education

Optional Slide

Facilitator Notes:

• Refer to the Brokers of Expertise Web site for an overview of CCSS modules available.

• Play the welcome message by Lupita Alcala, Deputy Superintendent of the Instruction and Learning

Support Branch at the California Department of Education.

2


Note to Facilitator:

• Remind participants to turn off cell phones or put in silent mode and refrain from texting.

• Review table handouts and supplies.

Talking Points:

• This first section of the module (Introduction, Overview, and Unit 1) will take approximately two hours to

complete.

• In the Introduction and Overview we will cover the following topics:

- Module Goals

- Overview of the CCSS for Mathematics

- Introduction to Units

- Metacognition and Reflection

- Pre-Assessment

3


Facilitator Notes:

Emphasize that the goals of this module are for teachers to understand the mathematical practice

standards and to be able to apply this knowledge to support the learning of their students.

• “SMP” refers to the eight practice standards as a group

• “MP” is used to refer to each individual standard

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Talking Points:

• First, let’s review some basic information about the CCSS.

• The Common Core State Standards Initiative was a state-led effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

• The CCSS are designed for the purpose of providing strong, shared expectations across states and allows the adopting states to develop, create, and share high-quality tools to support teaching and learning, including:

- Curricula

- Instructional materials

- Assessments

- Professional development programs

• The CCSS are:

- Internationally benchmarked with high-performing countries and are designed to prepare students for college and career readiness, allowing American students to successfully compete and collaborate with students around the world.

- Focused on readiness for college and career and provide a clear and consistent framework to prepare students for future academic and career success. They provide a common overview of the knowledge and skills K–12 students need, upon graduation from high school, to succeed in credit-bearing, academic college courses and in workforce training programs.

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Talking Points:

• The CCSS for Mathematics define what students should understand and be able to do. These standards

include expectations for both content and practice.

• The Standards for Mathematical Content, commonly referred to as “content standards”, include skills

and understandings that students should develop at each grade level (or within each course)

• The Standards for Mathematical Practice, commonly referred to as “practice standards”, identify the

processes and proficiencies that students should develop throughout their entire K–12 mathematics

education.

6


Facilitator Note:

Review list of unit titles on slide.

Talking Points:

• Using the lens of the SMP, this module will guide you through the teaching and learning of mathematics

to foster an understanding of the eight mathematical practices and why they are important for your

students.

• The rationale for this structure and grouping of the SMP is provided in Unit 1.

7


Facilitator Notes:

• Define “metacognition” on slide, indicating that participants will be journaling thoughts in a “Metacognitive

Journal” and collaborating to review and discuss reflections together.

8


Facilitator Notes:

• This activity will take approximately 5 minutes.

• Refer participants to the “Pre-Assessment” (Handout 1.0) and indicate that they should NOT collaborate on answering the questions.

• Facilitator can decide whether to review correct answers or wait until the end of the workshop to allow participants to learn over time if their responses were correct or not.

• An “I-Clicker” or similar tool may be used for group review with answers provided OR left open-ended, at the discretion of the facilitator. Participants should return the completed handout to their packets for future reference.

Talking Points:

• Before beginning the module, you will participate in a pre-assessment. This activity will assess your knowledge of the SMP prior to beginning the lessons.

• The assessment will be repeated upon completing the module activities to assess your learning.

Pre-Assessment answers:

1. c

2. c

3. d

4. a

5. c

6. True

7. False

8. False

9. False

10. True

9


Talking Points:

Now let’s begin Unit 1: Teaching and Learning the Standards for Mathematical Practice.

10


Facilitator Notes:

Review content on slide.

11


Talking Points:

• Observing students engaged in talking about and doing mathematics allows teachers to identify the SMP in action.

• We will watch a video [or three videos] of students engaged in doing mathematics. As you watch, take note of how the students are engaging in mathematics.

Facilitator Notes:

• Link to video(s) hosted on the Brokers of Expertise Web site: http://myboe.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=11776

• Videos are less than 4 minutes each.

• Options for viewing:

1) For multilevel groups, view all three videos as a group.

2) For homogenous grade span groups, view appropriate video as a group.

3) Divide participants in to three groups, primary, upper elementary, secondary. Each group will view the video at their grade span (as technology availability allows).

Grade 2: 3 min. 45 sec.



12

http://myboe.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=11776

http://myboe.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=11776


Facilitator Notes:

• After viewing the video, have participants discuss questions on slide in grade level groups (10 minutes)

• Have each group share out key ideas to the whole group (5 minutes)

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Talking Points:

•To establish a context for the SMP, this section will provide a brief overview of the Standards for

Mathematical Content.

•The CCSS focus on fewer topics to allow for a greater in-depth examination of mathematics concepts. As

a result of a clearly defined coherence across grade levels, students’ conceptual understanding develops

to allow for mastery of mathematical concepts.

•The content focuses on a rigorous set of skills at each grade level, enabling students to build a strong

foundational understanding of mathematics. For example, in the early grades there is a greater emphasis

on number concepts and skills. The key to student understanding is a balance of skill and procedure with a

clear focus on conceptual development.

•Standards that are rigorous, coherent, and focused provide better guidance to educators, students, and

parents about desired learning outcomes. The standards aim for clarity and specificity, and also stress

conceptual understanding of key ideas. In addition, the standards provide a balance of procedural skills and

conceptual development to support students’ mathematical understanding.

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Talking Points:

•The Illustrative Mathematics Web site offers interactive access to the content standards for K–8 by Content

Domains, High School Conceptual Categories, and the SMP.

•Note that Geometry is the only Domain that goes across the grades. Counting and Cardinality is only at

kindergarten and lays the foundation for numbers. Fractions start in grade three and are tied directly to number

concepts. Domains have a beginning and an end, with expectations that students learn the concepts and ideas

in depth.

•See progressions documents for further information: http://commoncoretools.me/category/progressions/


• Copy and paste the Illustrative Mathematics link into a Web browser to navigate the site with participants:

http://illustrativemathematics.org/standards/k8

• If participants have access to the Internet, have them take few minutes to navigate within the interactive graph

on the K–8 section of the Web site.

15


Talking Points:

• The Web site also shows the following graph which is accessible by Conceptual Category. The Modeling

Conceptual Category (not represented in the chart) includes standards in Higher Mathematics Courses

and is embedded throughout other Conceptual Categories indicated by a (?) symbol.

• In addition, examples of tasks can be viewed at the standards level.


• Copy and paste the Illustrative Mathematics link into a Web browser to navigate the interactive graph on the

Illustrative Mathematics Web site with participants: http://illustrativemathematics.org/standards/hs

• If participants have access to the Internet, have them take few minutes to navigate on their own.

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Talking Points:

• For additional information about the content standards, visit the mathematics learning progressions online

module on the Brokers of Expertise Web site. This module provides an overview of how the CCSS for

Mathematics kindergarten through grade eight learning progressions are sequenced across and within

grade-level spans (kindergarten through grade five and grades six through eight) and how to apply the

progressions to instructional practice.

• Visit also the “Tools for the Common Core Standards” Web site at the address provided on this slide.

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Facilitator Notes:

Slides 18–26 give information on the development and foundational underpinnings of the practice

standards.

Handouts for this section:

• Slide 19: Handout 1.2.1: “Principles and Standards for School Mathematics: Process Standards”

• Slide 20: Handout 1.2.2: “Intertwined Strands of Proficiency”

• Slide 23,24: Handout 1.2.3: “The Eight Standards for Mathematical Practice”

• Slide 26: Handout 1.2.4: “Self-Reflection Survey”

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Handout (optional):

“Principles and Standards for School Mathematics: Process Standards” (See Handout 1.2.1)

Talking Points:

• The SMP processes are derived from the National Council of Teachers of Mathematics process

standards, outlined in the publication, Principles and Standards for School Mathematics (2000).

• There are five process standards for mathematical practice, as listed on this slide.

• Take a few minutes to review Handout 1.1.1

19


Handout (optional):

“Intertwined Strands of Proficiency” (See Handout 1.2.2)

Talking Points

• The SMP proficiencies are based on the strands of mathematical proficiency specified in the National

Research Council’s report, Adding It Up: Helping Children Learn Mathematics (2001).

• The processes and proficiencies provided the basis for the development of the SMP; ways of thinking and

doing that lead to successful learning of mathematics content.

• Take a few minutes to review the handout titled, “Intertwined Strands of Proficiency”

20


Talking Points:

• The practice standards are about doing and using mathematics to foster reasoning and sense-making.

• Expertise with these practices emerges over time from opportunities and experiences provided in the

mathematics classroom.

21


Talking Points:

• Work on the SMP is ongoing.


• Review slide

22


Handout: “The Eight Standards for Mathematical Practice” (See Handout 1.2.3)


• Direct participants to handout and review the detail of each standard

MP1. Make sense of problems and persevere in solving them

Making sense and persevering are habits of mind needed by all students to be successful learners of

mathematics. Before a student can engage in mathematics, they need to make sense of what they are

being asked to consider.

MP2. Reason abstractly and quantitatively

Reasoning abstractly requires that students make sense of quantities and their relationships in problem

situations. Students decontextualize and contextualize mathematics; they translate problem situations into

symbols which they are able to manipulate and, as they manipulate the symbols, refer back to the problem

situation to make sense of their work.

MP3. Construct viable arguments and critique the reasoning of others

Constructing arguments requires that students use stated assumptions, definitions, and previous results.

They make conjectures, justify their conclusions, and communicate them to others. They respond to the

arguments of others.

MP4. Model with mathematics

Modeling with mathematics requires that students make assumptions and approximations to simplify a

situation, realizing these may need revision later, and that students interpret mathematical results in the

context of the situation and reflect on whether they make sense.

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Note to Facilitator: Continue from previous slide.

Talking Points:

MP5. Use appropriate tools strategically

Using tools strategically requires that students are familiar with appropriate tools to decide when each tool

is helpful, know both benefits and limitations, detect possible errors, and identify relevant external

mathematical resources and use them to pose or solve problems.

MP6. Attend to precision

Precision refers to the accuracy with which students use mathematical language and symbols as well as

precision in measurement.

MP7. Look for and make use of structure

Looking for structure refers to students’ understanding and using properties of number systems, geometric

features and relationships, and patterns of a variety of types to solve problems.

MP8. Look for and express regularity in repeated reasoning

Looking for regularity in repeated reasoning refers to the process of noticing repeated patterns or attributes

and using those to abstract and express general methods, expressions or equations, or relationships.

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Talking Points:

• The SMP define what it means for students to be mathematically proficient.

• In order for the practice standards to be developed, the approaches should be embedded in all

mathematical activities such as instruction, discussion, and investigation; not just during problem-solving

sessions such as “Problem of the Day.”

• This does not mean that all eight SMP are in play at all times.

• Engagement with the SMP is not experienced in isolation or for special times within the class period.

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Handout:

“Self-Reflection Survey” (See Handout 1.2.4).


• Administer Self Reflection Survey or assign as writing prompt

• Save survey or writing entries for comparison with end of module response

Talking Points:

• At the end of the module, you will return to this survey to see how your participation in this module has

impacted your confidence in teaching and learning the eight SMP.

• The unit continues with a look at connecting content and practice standards, organizing for

implementation and meeting the needs of all students.

26


Talking Points:

• The next few slides will provide an overview of how to achieve meaningful learning for ALL students through

the interaction of both practice and content standards for mathematics.

Notes to Facilitator:

Section includes:

• Slide 27: Interaction of Practice Standards and Content Standards

• Slide 28: Meaningful Learning

• Slide 29: Focus and Coherence (video)

• Slide 30: Time to Talk

• Slide 31: Bringing Structure

• Slide 32: The Structure

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Talking Points:

• Meaningful learning is likely to occur when students have access to a coherent and connected curriculum

in an environment that promotes discourse, reflection, collaboration, and use of appropriate tools while

working on challenging mathematics.

• This involves doing mathematical problems and tasks which necessitate problem solving, reasoning, and

sense-making.

• Student engagement with both content and practice is needed for deep learning.

28



• Video length: 1:13 minutes

• Video also available at:

http://www.youtube.com/watch?v=9pKcO9E4Flw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=10&featur

e=plcp

Talking Points:

• The video, “Mathematical Practices, Focus and Coherence,” featuring Jason Zimba (one of the lead

writers of the CCSS for Mathematics) underscores the interrelation of the two types of standards,

mathematical content and mathematical practice.

29

http://www.youtube.com/watch?v=9pKcO9E4Flw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=10&feature=plcp

http://www.youtube.com/watch?v=9pKcO9E4Flw&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=10&feature=plcp



Facilitate a discussion based on the questions presented.

• Step 1 Options:

Elbow partners

Small groups

Individual quick write

• Step 2: Full group discussion

30


Talking Points:

• Many of the processes and proficiencies in the individual practice standards overlap, and several may be

used together in solving a problem or engaging in a task.

• Additionally, most of the practices can be applied to most of the content standards. An attempt has been

made to bring structure to the SMP.

• In order to avoid “doing nothing” when integrating the practice and content standards, Bill McCallum,

one of the lead writers of the CCSS for Mathematics, grouped the standards to bring a higher order of

structure to the standards.

31


Talking Points:

• The eight practice standards have been usefully grouped into four pairs which provides structure to the

mathematical practices just as the clusters and domains bring structure to the content standards.

• This structure serves as a way to think about and plan for implementation of the SMP as well as to select

tasks and look for evidence of students’ demonstration of engagement.

• It makes logical connections across the standards and takes advantage of the overlap of practice

standards to provide needed focus.

• The structure is shown in the diagram. It has also been used to organize the units within this module.

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Talking Points:

• The next group of slides provides information on connecting content and practices.


The section includes:

• Slide 33: Connecting Content and Practice

• Slide 34: Impact of Understanding

• Slide 35: Importance of Understanding

• Slide 36: Possible Starting Points

• Slide 37: An Example

• Slide 38: Grain Size

• Slide 39: Organizing for Learning

• Slide 40: Progress Check

Handouts for this section:

• CCSS for Mathematics (See Handout 1.3.1).

33


Facilitator Notes:

• Allow time to read slide.

Talking Points:

• In this respect, those content standards which set an expectation of understanding are potential “points of

intersection” between the Standards for Mathematical Content and the Standards for Mathematical

Practice.

34


Facilitator Notes:

• Allow time for participants to read silently. May follow up with oral reading.

Talking Points:

Understanding is important in implementation of the CCSS for mathematics.

35


Talking Points:

A certain level of understanding is needed in order to employ the SMP to deepen learning.

36


Talking Points:

• In this standard (Grade 4, Number and Operations—Fractions, Standard 3a), over-reliance on an

algorithm may make it impossible for a student to explain, for example, why reference to the same whole

is necessary when adding fractions or to build on notions of equivalence or knowledge of unit fractions to

justify a solution.

• Therefore, the concepts delineated at these points of intersection are important; as is providing time,

resources, and focus for their development. Setting the points of intersection as a priority can only lead to

improved teaching and learning of mathematics.

Facilitator Notes:

Activity follow up:

• Direct participants to locate other content standards which set an expectation of understanding.

• Pose question: What connections can be made between SMP and the content standards for the specific

standard chosen?

37


Talking Points:

• Phil Daro, one of the lead writers of the CCSS for Mathematics, refers to proper grain size as the unit at

which it makes most sense to organize mathematics for learning.

• Daro suggests that teachers look at units or chapters rather than lessons when planning for instruction

and assessment of the standards.

38



• Review slide

39


Facilitator Notes:

• Provide a brief review and direct participants to reflect on the prompt.

• If using a journal, provide time to reflect and write.

• Facilitate a discussion based on the questions presented.

- Step 1 Options:

Elbow partners

Small groups

Individual quick write

- Step 2: Full group discussion

40


Notes to Facilitator: Review slide

Slides 41–50 contain information on meeting the needs of all students.

• Slide 41: Meeting the Needs of All Students

• Slide 42: Language Learning and Mathematics

• Slide 43: Students with Disabilities

• Slide 44: Resources

• Slide 45: Supporting English Learners: English Language Development Standards

• Slide 46: Understanding Language

• Slide 47: Teaching Els Conceptually (video link)

• Slides 48-49: 21st Century Skills

• Slide 50: Learning Objectives Revisited

Talking Points:

• The CCSS for Mathematics demands that the needs of ALL students are addressed.

• The units of this module will give you the opportunity to think about differentiation strategies to meet the needs of all learners, including students with special needs, English learners, under-performing students, and gifted and talented students.

41


Talking Points:

• The SMP emphasize doing mathematics. Therefore, all students must have an opportunity to

demonstrate learning in an environment that structures timeframes in which to talk, access tools, work on

challenging tasks, and other activities supported in the SMP.

• Judit Moschkovich, professor of mathematics education at Stanford University, whose research examines the

relationship between language learning and math, recommends ways to support the learning of language in

conjunction with the teaching of mathematics. The instructional strategies shown on the slide can be applied

for ALL students of mathematics (Moschkovich, 2012).

42


Facilitator Notes: Read quote.

Talking Points:

• Students with disabilities will receive the support they need to do mathematics. These accommodations

include:

- Instructional supports for learning — foster student engagement by presenting information in

multiple ways and allowing for diverse avenues of action and expression

- Instructional accommodations — changes in materials or procedures which do not change the

standards but allow students to learn within the framework of the CCSS

- Assistive technology devices and services — ensure access to the general education curriculum

and the CCSS

43


Facilitator Notes:

May choose to distribute “Application to Students with Disabilities” and “Teaching Common Core Math

Practices to Students with Disabilities” as a handout.

Talking Points:

• The CCSS publication, “Application to Students with Disabilities”, addresses how the standards can apply to

students with disabilities and their special needs, and ensures access to the general curriculum.

• “Teaching Common Core Math Practices to Students with Disabilities” offers alternatives to direct instruction

for special education teachers.

• The “Special EDge” is a publication of the California Department of Education’s Special Education

Division. Read the issue devoted to the CCSS.

• The Council for Exceptional Children (CEC) views the CCSS as an opportunity to provide access to the

general curriculum to all students with disabilities. The journal article, “Teaching Mathematics CCSS to

Students with Moderate to Severe Disabilities”, provides teachers with a six-step approach to providing

instruction to students with moderate and severe disability aligned to the new CCSS.

• Another CED publication, “Six Principles for Principals to Consider in Implementing CCSS for Students

with Disabilities,” provides CCSS implementation guidance in the instruction and assessment of students

receiving special education services.

44



Link for overview of ELD standards: http://www.cde.ca.gov/sp/el/er/documents/sbeoverviewpld.pdf

Talking Points:

• In order to ensure equity in the mathematics classroom, the needs of English learners must be

considered. The CCSS for Mathematics speaks to teaching mathematics for understanding. Part of this

understanding is embedded in language proficiency for mathematics.

• California has revised and updated its English Language Development Standards for California Public

Schools: Kindergarten through Grade Twelve. [Review slide quote]

• HANDOUT: Overview of the California English Language Development Standards and Proficiency Level

Descriptors

• OPTIONAL HANDOUT: “Mathematics, the Common Core, and Language: Recommendations for

Mathematics Instruction for ELs Aligned with the Common Core ” by Judit Moschkovich (See Handout

1.4.2).

Available at http://ell.stanford.edu/sites/default/files/pdf/academic-papers/02-

JMoschkovich%20Math%20FINAL.pdf

45

http://www.cde.ca.gov/sp/el/er/documents/sbeoverviewpld.pdf

http://www.cde.ca.gov/sp/el/er/documents/sbeoverviewpld.pdf

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/02-JMoschkovich Math FINAL.pdf






Talking Points:

• Understanding Language is a initiative at Stanford University that focuses on heightening awareness of the language and literacy issues embedded within the new standards. Judit Moschkovich is part of the leadership team for this initiative. Her publication, Mathematics, the Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the Common Core, provides principles to guide educators in supporting reasoning and sense-making of mathematics for English learners. [http://ell.stanford.edu/sites/default/files/pdf/academic-papers/02 JMoschkovich%20Math%20FINAL.pdf]

Guiding Principles:

• Focus on students’ mathematical reasoning, not accuracy, in using language. Focus instruction on uncovering, hearing, and supporting students’ mathematical reasoning, not on accuracy of language.

• Shift to a focus on mathematical discourse practices; move away from simplified views of language. The focus of classroom activity should be on student participation in mathematical discourse practices (explaining, conjecturing, justifying, etc.). Instruction should move away from simplified views of language as words, phrases, vocabulary, or a list of definitions.

• Recognize and support students to engage with the complexity of language in mathematics classrooms.. Language in mathematics classrooms is complex and involves:

- Multiple modes (oral, written, receptive, expressive, etc.). - Multiple representations (including objects, pictures, words, symbols, tables, graphs, etc.) - Different types of written texts (textbooks, word problems, student explanations, teacher explanations, etc.) - Different types of talk (exploratory and expository) - Different audiences (presentations to the teacher, to peers, by the teacher, by peers, etc.)

• Treat everyday language and experiences as resources, not as obstacles. It is not useful to dichotomize academic and everyday language. Instead, instruction needs to consider how to support students in connecting the two ways of communicating, building on everyday communication, and contrasting the two when necessary.

• Uncover the mathematics in what students say and do. Materials and professional development should support teachers to prepare them to deal with the tensions around language and mathematical content, in particular: How to uncover the mathematics in student contributions; When to move from everyday to more mathematical ways of communicating; When and how to approach and develop “mathematical precision. ”

Using the above principles as guides, the standards may be implemented in ways that all students achieve and are equipped to meet the challenges of learning mathematics.

46









Video available on the Understanding Language Web site at:

• http://ell.stanford.edu/publication/mathematics-common-core-and-language

• http://www.youtube.com/watch?v=gUfpnIbq4TA

Talking Points:

• Let’s take a few minutes to watch Moschkovich’s video on teaching mathematics for conceptual

understanding with English learners (3:49 minutes).

• ELs may not speak like mathematicians right away, but teachers can build on the mathematical reasoning

they're already doing.

• As an extension activity, you may read the entire paper by Judit Moschkovich, “Mathematics, the

Common Core, and Language: Recommendations for Mathematics Instruction for ELs Aligned with the

Common Core” or her classroom vignette based on a lesson presented in a third grade bilingual

classroom in California.

47


Talking Points:

• At the heart of the CCSS for Mathematics is a mandate to prepare ALL students for college, career, and

life. To do so effectively, students must have an opportunity to develop the skills, processes, and

knowledge that will prepare them for the challenges that they will face. These skills are known as 21st

Century skills.

(1) Creativity and innovation—including, but not limited to thinking creatively, working creatively with

others, and implementing innovations

(2) Critical thinking and problem solving—including, but not limited to, reasoning effectively, using

systems thinking, making judgments and decisions, and solving problems

(3) Collaboration—including, but not limited to, working effectively in diverse teams, adapting to change

and being flexible, demonstrating initiative and self-direction, working independently, demonstrating

productivity and accountability, and demonstrating leadership and responsibility

(4) Communication—including, but not limited to, communicating clearly and effectively through

reading, writing, and speaking.

(5) Construction and exploration of new understandings—knowledge through the integration of

content from one subject area to another and multiple modes for demonstrating innovative learning

48


Talking Points:

• 21st Century skills are strongly related to the SMP. The Partnership for 21st Century Skills (P21) provides

examples of this in its publication, P21 Common Core Toolkit: A Guide to Aligning the Common Core

State Standards with the Framework for 21st Century Skills (p. 8).

• Engagement in the SMP allows for the development of 21st century skills, as shown in this slide.

P21 Web site: http://p21.org/index.php?option=com_content&task=view&id=1005&Itemid=236

49

http://p21.org/index.php?option=com_content&task=view&id=1005&Itemid=236




Talking Points:

• Let’s revisit our learning objectives. At this point you should be able to…

50


Facilitator Note:

• Facilitate a discussion regarding the questions or assign a written reflection followed by sharing.

Talking Points:

• By this time, you should be able to do the following: [Review slide]

Facilitator Note:

Slides 51–53 close Unit 1 and allow time for reflection and/or discussion

• Slide 51: Talk about …

• Slide 52: Think about

• Slide 53: Looking Ahead

51

California Department of Education 52


• Unit 2: Overarching Habits of Mind (MP 1 and MP 6)

• Unit 3: Reasoning and Explaining (MP 2 and MP 3)

• Unit 4: Modeling and Using Tools (MP 4 and MP 5)

• Unit 5: Seeing Structure and Generalizing (MP 7 and MP 8)

• Unit 6. Summary, Next Steps, and Resources

53


0 minutes (TRANSITION SLIDE)

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